Hello group, after about 140 days on an Athlon XP 2600 with the use of a combined sieving and prp program written by Jens Kruse Andersen, I found a new ...
Main page ( http://www.opertech.com/primes/k-tuples.html ) The latest updates have been posted, with improvements to more than 2200 widths. Currently there are...
Hello all: I have obtained this result: DivisorSigma[2k,m]/DivisorSigma[k,m] is integer if and only if m is a perfect square DivisorSigma[k,m]=sum[d^k, d...
No prime p is (p-1)modulo 4, as primes that are(p-1)modulo 2 are [(p-1)/2]modulo4, and if the order of pmodulo2 is less than p-1, then the modulo4 of p is...
Hi all, I am now ready to publish Carol/Kynea numbers. How do i go about doing that/ What journal should I submit to/ Is there a special format? Any help...
Powers of Two Numbers are 1 21 421 8421 168421 32168421 6432168421 1286432168421 ... The conjecture is that 421 is the only Power of Two Prime. The other...
Suppose you are trying to approximate sum over large primes p of a(p) where a(p) is some monotonically decreasing to 0 function of p. Instead of writing...
Hi all, I just realixzed that the 40th and largest Carol Prime n=253987, was reported on the prime database on Carol's birthday, May 7, 2007... ... Moody...
Hello, the k-tuplets page is down since several days. In addition Tony Forbes' e-mail adress @ltkz.demon.co.uk is not working. Does anyone know an actual...
Hi, Group, et. al. I have a rather simple observation that may imply that the number of Fermat primes is finite. Conjecture: If a Fermat number of the form...
I make the following statement based only on a limited number of calculations. I was unable to find any web references. Has anyone come across anything like...
I've programmed the Fermat prime number sieve and tested it out on a few different ranges. If the occasion ever arose to factor all numbers in an interval,...
2^(2^m) + 1 mod prime 3 cannot divide any number in this series because (2 -1)^2 + 1 = 2 5 cannot divide any number in this series except 5 because (2 -...
Who can help me calculating up to 10 exact decimal places sum (1/n^(1-1/n) - 1/n) sum (1/p^(1-1/p) - 1/p) sum (ln(n) / n^2) sum (ln(p) / p^2) n=positive...
We fill the array with it's index up to the length of the table. For example if we wish to use the Fermat prime number sieve to find the primes < 250, we set...
The divergence of sum(1/2^ln n) and sum(1/2^ln p) can easily be proven. How can be proven that sum(1/3^ln n) and sum(1/3^ln p) converge? (IF they do. What are...
The new version of RMA.NET, has been extensively tested, and is now ready for release. This windows program is by far the fastest prime number software ...
Hello All, I generated the following fractal plot: http://www.isenbek.com based on the first 10,000 primes. I was wondering if anyone has seen this before, and...
Let p be a large prime, and g a generator of Z/pZ. Let u<p be non-zero modulo small prime q. From g^u (mod p), is it ever possible to tell anything more about...
I was searching for an interesting note I've read years ago. Here it is: http://www.mathpages.com/home/kmath222.htm Hugo Scolnik [Non-text portions of this...
I´d like to share a little concept for ACCOUSTICAL FACTORIZATION by using the relation between tones and overtones on strings, many guitarplayers might be...
... The density of numbers being nth-powerfree is 1/zeta(n), where zeta is the Riemann Zeta Function. So, for squarefree numbers, we have your probability is...
What is the probability of a number being square free... it seems that the more square free numbers than the non-square free numbers for big numbers. Would be...
How are the Smarandache folks able to get away with renaming everything "smarandache this" and "smarandache that" when most of the mathematical miscellanea...
maybe... let Z = 2^(2^(p+1))+1 ; p is prime Z is prime iff [Z (mod (2^p+1))] == 2^q ; for some q for p = 2, 3,..., next??? eg. p=2, 2^8+1 mod 5 == 2^1 and... ...
An interesting extension of Patrick De Geest's Table is where 10^n+p and p are both prime (the first instance) The table begins: n---------p ============= ...
